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Exact Binary Projections for Array-RQMC: Joint Laws and Pathwise-Preserving Execution

Aoi Kawasaki

Published Sep 13, 2026• 0 citations
Publisher

Abstract

Exact Binary Projections for Array-RQMC: Joint Laws and Pathwise-Preserving Execution Aoi Kawasaki. Preprint; not peer reviewed. Contribution For a specified two-dimensional Sobol net with linear matrix scrambling and a digital shift, the complete rank-ordered binary innovation vector is uniform over exactly N outcomes at N = 2^m paths. An odd mask and a fair bit describe the law, requiring m independent fair bits per step under the stated ideal randomization model. Independent adjacent antithetic pairs have the same covariance but need not have the same higher-order law; exact nonlinear witnesses give variances 0 versus 2 and 4 versus 2. This characterization enables direct generation without generating unused coordinates or sorting the point set. A second rewrite maintains exactly the reference state order for stopped scalar binary chains with monotone branches, including absorption and floating-point ties. Measured results and limits Across eight fixed benchmark cases in two input encodings, state-order maintenance reduced warm execution time by 37.2% at N = 512 and 67.5% at N = 4,096 relative to direct binary generation with full state sorting. The encodings do not create sixteen independent model laws. The measurements are from one CPU/software stack, not a held-out hardware or dynamics study. The joint-law equivalence of the library and direct generators is an ideal-law statement, not equality under the same finite integer seed. Direct and order-maintained execution do preserve the same finite-seed trajectories and outputs under the stated arithmetic conditions. No new convergence rate or universal variance advantage is claimed. Comparisons with the measured CRN and antithetic implementations remain workload- and reuse-dependent. Avoidable mask initialization was included in the measured baselines; it is not an intrinsic CRN cost. Startup and calibration can outweigh warm-time savings. The publication retains those recorded costs. Included materials and reproducibility scope The record contains the manuscript PDF and a self-contained reproducibility capsule with manuscript/build sources, three array kernels, 19 tests, saved table/figure inputs, two figures, dependency versions, and SHA-256 inventories. The tests include exact finite enumeration, within-project separate reference implementations, absorption and floating-point tie checks, and saved-data arithmetic. They are not third-party peer review. The capsule does not include every raw calibration/validation observation, bootstrap sample, timing round, or baseline/calibration driver. Regenerating saved tables and figures is not a rerun of the full original experiment. No GPU, pretrained model, private workspace, or external dataset is required. Rights and disclosure Publication materials and saved data: CC BY 4.0. Code: MPL-2.0, with per-file scope in LICENSES.txt. Generative-AI assistance is disclosed in the manuscript. The version-specific archival identifier is doi:10.5281/zenodo.22728405.

DOI
10.5281/zenodo.22728404

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Exact Binary Projections for Array-RQMC: Joint Laws and Pathwise-Preserving Execution Aoi Kawasaki. Preprint; not peer reviewed. Contribution For a specified two-dimensional Sobol net with linear matrix scrambling and a digital shift, the complete rank-ordered binary innovation vector is uniform over exactly N outcomes at N = 2^m paths. An odd mask and a fair bit describe the law, requiring m independent fair bits per step under the stated ideal randomization model. Independent adjacent antithetic pairs have the same covariance but need not have the same higher-order law; exact nonlinear witnesses give variances 0 versus 2 and 4 versus 2. This characterization enables direct generation without generating unused coordinates or sorting the point set. A second rewrite maintains exactly the reference state order for stopped scalar binary chains with monotone branches, including absorption and floating-point ties. Measured results and limits Across eight fixed benchmark cases in two input encodings, state-order maintenance reduced warm execution time by 37.2% at N = 512 and 67.5% at N = 4,096 relative to direct binary generation with full state sorting. The encodings do not create sixteen independent model laws. The measurements are from one CPU/software stack, not a held-out hardware or dynamics study. The joint-law equivalence of the library and direct generators is an ideal-law statement, not equality under the same finite integer seed. Direct and order-maintained execution do preserve the same finite-seed trajectories and outputs under the stated arithmetic conditions. No new convergence rate or universal variance advantage is claimed. Comparisons with the measured CRN and antithetic implementations remain workload- and reuse-dependent. Avoidable mask initialization was included in the measured baselines; it is not an intrinsic CRN cost. Startup and calibration can outweigh warm-time savings. The publication retains those recorded costs. Included materials and reproducibility scope The record contains the manuscript PDF and a self-contained reproducibility capsule with manuscript/build sources, three array kernels, 19 tests, saved table/figure inputs, two figures, dependency versions, and SHA-256 inventories. The tests include exact finite enumeration, within-project separate reference implementations, absorption and floating-point tie checks, and saved-data arithmetic. They are not third-party peer review. The capsule does not include every raw calibration/validation observation, bootstrap sample, timing round, or baseline/calibration driver. Regenerating saved tables and figures is not a rerun of the full original experiment. No GPU, pretrained model, private workspace, or external dataset is required. Rights and disclosure Publication materials and saved data: CC BY 4.0. Code: MPL-2.0, with per-file scope in LICENSES.txt. Generative-AI assistance is disclosed in the manuscript. The version-specific archival identifier is doi:10.5281/zenodo.22728405.
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Joint force and coherence constraints are implemented for one specified Gaussian Diósi–Penrose generator in a fixed finite-time protocol. The analysis retains kinetic energy, correlated two-body noise, three-dimensional wave packets, and local decoding followed by tracing out motion. A trusted normalized initial-force bound of 0.995 restricts the common smearing scale from above. Uniformly over the remaining positive scales, the local statistic has Newton mean greater than 0.9965 and DP absolute mean less than 0.4581. An entanglement witness from the same measurement record also has a positive prediction gap greater than 0.03761, but entanglement is not necessary for this model exclusion. The small-smearing argument bounds full coherence blocks by an early completely positive instrument and includes subsequent interacting evolution in the bound. The general force–decoherence principle is known; the contribution is the controlled finite-readout implementation. This is a conditional nonrelativistic theoretical result with trusted ideal preparation, force calibration, and readout, not an empirical exclusion or a general certification of quantum gravity. The companion archive includes the full LaTeX source, standalone Python checks, exact rational certificates, and reproducibility instructions. The work has undergone internal checks, not independent peer review. Generative-AI assistance is disclosed in the paper. Licensing: the manuscript PDF, LaTeX source, documentation and numerical records are licensed under CC BY 4.0. The Python software and its embedded tests are licensed under MIT. These licenses apply to separate file categories, as specified in the companion archive; they are not alternative licenses for every file.